[R-sig-ME] zero Inflation in glmmadmb

[Ben Bolker]

  I'm going to take the liberty of replying by way of r-sig-mixed-models,
as this is a generally useful question ...

On 13-07-29 04:08 AM, Bartzke, Gundula wrote:
> Dear professor Bolker,
> 
> I have applied the glmmadmb command to apply a zero-inflated
> negative binomial model. The outcome is different to zero-inflated
> models using the pscl package. Why is there only one set
> coefficients in the summary instead of two for each of the
> component models and how can the coefficients be interpreted? I
> suspected that glmmadmb may apply a model similar to this one: 
> http://hosho.ees.hokudai.ac.jp/~kubo/Rdoc/library/VGAM/html/zinegbinomial.html
> 
At present glmmadmb fits only a constant-zero-inflation model,
corresponding
to a zeroinfl model of y~...|1 (zeroinfl's default is to make the
conditional mean and zero-inflation models the same). This is the
same as VGAM's default (i.e., with the 'zero' parameter excluded:
'zero=NULL' fits a model where conditional mean, dispersion, _and_
zero-inflation all use the same covariates).

  The results (see below) seem to be perfectly consistent.

> but the results are neither consistent. Also I am uncertain about
> the alpha-value in the negative binomial component of the hurdle
> models. It seems to be the same as theta (or k). I thought alpha is
> 1/k. For the example data they are nearly identical but for my own
> data they differ. Could you please clarify this?

  The terminology is highly variable.  In this case alpha is indeed
the same as theta/k/size ...

library(pscl)
library(glmmADMB)
library(VGAM)

Owls <- transform(Owls,
                  Nest=reorder(Nest,NegPerChick),
                  logBroodSize=log(BroodSize),
                  NCalls=SiblingNegotiation)

## compare all three models, with constant zero-inflation probability
##  (default for VGAM and glmmADMB)
fit_zinb <- zeroinfl(NCalls~(FoodTreatment+ArrivalTime)*SexParent|1,
                     data=Owls, dist="negbin")
fit_zinbadmb <- glmmadmb(NCalls~(FoodTreatment+ArrivalTime)*SexParent,
                         data=Owls,
                         family="nbinom", zeroInfl=TRUE)
fit_zinegbinomial <- vglm(NCalls~(FoodTreatment+ArrivalTime)*SexParent,
                          data=Owls, zinegbinomial())

summary(fit_zinb)
summary(fit_zinbadmb)
summary(fit_zinegbinomial)

## glmmADMB fits zero-inflation and alpha on non-transformed scales
qlogis(fit_zinbadmb$pz)
log(fit_zinbadmb$alpha)

## 'alpha' (glmmADMB) = 'theta' (zeroinfl) = 'size' (VGAM)
## 'zero-inflation' = 'zero-inflation' = 'pstr0' (VGAM)